The opposite of "brings pressure to bear upon" can be phrased as "relieves pressure." This can involve actions such as easing tensions, reducing stress or anxiety, or providing support and comfort. Rather than exerting influence or control over a situation, reliving pressure involves creating a sense of calm and stability. Other possible antonyms might include "avoids confrontation," "maintains neutrality," or "remains passive." These expressions all suggest a lack of interference or influence, allowing situations or individuals to unfold naturally without external pressure or manipulation.